so both level's achievements for that are linked? as in, in the achievement list, both the Defeat Lord Coleem in Heart of Gold achievements in the campaign go to the same achievement in the achievement list.

Yes Coleem can be vanquished in Heart of Gold level 2. As such the achievement for defeating him in the Heart of Gold campaign can be awarded on either Level 2 or 4 (where he reappears if he was not previously defeated)